CCE Series NiathenatiGs Term tive amidea CCE Series Summative Assessment MATHEMATICS (Continuous and ComprehensiveEvaluation) Term 1: Summative Assessment-1 Formative Assessment- 1&2 Class IX Model Question Papers O Multiple Choice Questions O Short Answer QuestionsS OLong Answer Questions O Project Formative Assessment O Activity O Rapid Fire Quiz SucceSS OOral Questions O Paper Pen Test O Multipe Choice Quetions

CCE Series Mathematics (ContinuOus and Comprehensive Evaluation] Term 1: Summative Assessment- 1 TSummative Assessment -Model Question Papers -Multiple Choice Questions Formative Assessment - 1 & 2 -Short Answer Questions -Long Answer Questions IFormative Assessment -Project -Activity -Rapid Fire Quiz -Oral Questions Paper Pen Test -Multiple Choice Questions KGlobgl Publicotions Pvt. Ltd. gode.N.!ns Class. IX TIÍdea

Contents UNT- I Number Syxtew Sumumative and oatve Asnessnwnt I., Roal Numtrs UNIT- I| Algebra 378S3 5 UNIT ||l Geometry 8, lInrohuetion to Buclid's (Geomery onnaive Anesment t. Lines and Angls. 5. Triangles.... lomaive :\seuct 'TERM-| UNIT - IV Coordinate Geometry 6. Coordinate Geometiry tomative Avsessnent UNIT -V Mensuration 7. Area ofriangks-Heron's lormula. Formative Asessoent LatestCBSE Sample aper Model Question Vapers (Sokel) . Model Qucstion lapers (Unsolve).... )) 58 62 77 8-1 .96 103 I18 130 135 1-45 I88

Time: 3 hours General Instructions: 1. Al questions are comþulsory. 1ne question paper consists of 34 auestions divided into 4 sctions. A. B. Cand D. Section -A comfprises of 8 questto5 of 1 mark each. Section - B Combrises of 6 estions of 2 marks each. Section-G comprses of 10 uestions of 3 marks each and Section-D comprises of 10 questions of 4 marks each. D. eslon numbers 1 to 8 in Sectiom-A are multible choice questions where you are to select one COTTea opLOTn Od of the given four. 5. Use of calculators is not permitted. Model Question Paper (Unsolved) -1 1. There is no overall choice. However, internal choice has been trovided in 1 question of twO marks, 3 questions of Zhree marks each and 2 questions offour marks each. You have to attempt only one of lhe alernattves tn all such questions. (a) terminating Summative Assessment - I Question numbers I to 8 carry l mark each. I. Decimal representation of a rational number cannot be (c) non-terminating repeating (a) 0 Mathematics (a) 1 2. IfP(x)= *²-2/2x +1, then P (2/2) is equal to (a) 100 3. If +2=-1 (*,y+0), the value ofx'-y° is (c) J24 cm 4. The value of (525)* -(475) is (b) I (a) 316 cm² (c) 296 cm? (6) -1 (b) 10000 Section -A 6. The area of trapezium in Fig. I is (b) 48 cm (d) 4 cm 5. An isosceles right triangle has area 8 cm². The length of its hypotenuse is (a)J32 cm (b) 306 cm? (d) 286 cm? (b) non-terminatúng (d) non-terminating non-repeating (c) 4/2 Maximum Marks: 90 (c) 0 (c) 50000 9 cm () 8/2 +1 (d) 100000 28 cm 40 cmn: Fig. 1 ) 15 cm VKGotat pbhcatans P e

7. Axioms are assumed (a) universal I truths in all branches of Mahemaics (c) theorcms truc? (a) DF =5 cm, ZT = 60° (c) DE = 5cm, ZF= 60° 8. It is giventhat MBCe AFDE and AB = 5 cm, ZB=40°and A =80°Then which of the following is false. Justily your answer. Ouestion numbers 9 to 14 carry 2 marks each. /147 9. - is not a rational number as y47 and w75 are not integers. State whether the statement is true or /75 10. Without actually calculating the cubes, find the value of 48-30- 183. 1 Ifx +l is a factor of ax +**-2x +4a-9, find the value of a. OR In Fig. 3, if l|| m, then find x. Simplify: 3 19. Solve the equation a –1l5=25 and state which axiom do you have. 13, In Fig. 2, what value of x will make POR a straight line? (6) DF =5 cm, ZE = 60° -2 (d) DE = 5 cm, ZD = 40° 93x 27 2 36 x3 3 SR OR A (0, -3), B(3, 4), C(5, 0), D(-2, 2) (4x-36)° 14. Which of the following points will lie on x-axis or y-axis? ©VK Global Publications Pvt. Ltd. Section- B Flg.2 (b)universal truths specific to geometry (d) definitions Question numbers 15 to 24 carry 3 marks each.stv atete 15. Find three rational numbers between and 16. Express 0.123 in the form of. (3x + 20)° 17. Using an identity evaluate (998)° Model Question Papers 3 Section -C 9 3 189 44° Flg. 3

190 Mathematics IX : Term - I 18. Find the valuc of k so that 2x-lbea factor of8z4 + 4y-16z+10z * Factorise: 1-64a -12a + 48a 19. In Fig. 4, if AC= BD, using an Euclid's axiom show that AB =D. OR 20. In Fig. 5, BA||ED andBCl|EF. Show that ZABC= DEF., 25. In Fig. 6, if PQ||RS, ZMXQ = 135° and ZMYR = 40°, find XMY. B OR P R 21. In Fig. 7, D and E are points on side BC of a AABC such that BD = CE and AD = AE. Show that AABD= AACE. V2+1 If x = /2 -1 22. In Fig. 8, PQ = PR and ZO= ZR. Prove that APOS APRT. (b) four times its supplement. 23. Find the measure of an angle which is 26. Simnplify: (a) one-fourth of its complement. Fig. 4 40° and y = Fig. 6 Question numbers 25 to 34 carry 4 marks each. 7/3 V10 +/3 /2-1 /2 +1 OR Fig. 8 2/5 24. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle. S Ifa =5-2/6, then findthe value of Va Section - D R 3/2 J6 +V5 V15 +32 find the value ofx*+y +xy. B D tt Fig.7 m OVK Global Publications Pv LId

27. Find the product (* -2y-z)(*? +4y'+z² +2ry +xz -2yz) 28. Factorise: (2r +3)3 -(2x -3y) OR Factorise: x* +2* y -2y-1 29. Ifz +=83, find the value of z 30. From the Fig. 9, answer the following: (i) Coordinates of point C. (ü) The point identified by the coordinates (-3, -7). (iii) The abscissa of the point E. (iv) The ordinate of the point F. (u) Coordinates of point O. (vi) The quadrant in which point G lies. Fig. 9 (vin) The perpendicular distance of the point A from the x-axis. OF (vii) The perpendicular distance of the point B from the y-axis. 31. Prove that the sum of the angles of a triangle is 180°. VK Global Publications Pvt. Ltd. Model Question Papers 191 S2. In a AABC, the angle bisectors of the B and 2C meet at 0. IfZA =60°, then find the value ofZBOC. 33. A transversal intersect two parallel lines. Prove that the bisectors ofany pair of correspondingangles so formed are parallel. Ot. Ifthe bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

Time: 3 hours General Instructions: As given in ModelQuestion Paper (Unsolved)l Question numbers 1 to 8 carry 1. The value of 19.999.... 10 4. 2 (a) 21 (a) 24 Model Question Paper (Unsoved)-2 Summative Assessment - ! 2. Which of the following is a polynomial? (a) ** 2 (a) (a) 40/15 cm² 3. Ifx-20 is divided by x +1, the remainder is -y² 4 (b) cm? Mathematics If x +y=9 and *y = 20, then the value of x 7. Greeks emphasised on (a) inductive reasoning (c) botha and b l mark each. 1999 1000 (6) /2x -1 VK Global Publications Pvt. Ltd. in the form , where and g are integers and q #0 is (b)21 (b) 41 (b) 5. The sides of a triangle are 13 cm, 17 cm and 20 cm. Its area is Section - A (b) 20V30 cm² 8. Complementary angle of 35° is (a) 145° (b)55° 6. The area of an isosceles triangle having base x cm and equal side y cm is 2 *y2 cm² Question nunbers 9 to 14 carry 2 mnarks each. (c) 2 (c)x2+ (c) 20 (c) 81 (iü) 10.124124.. 3 " (c) 60V10 cm² (c) x4y²-*² cm? Section - B (b) deductive reasoning (c) 325o Maximum Marks: 90 9. Classify the following numbers as rational or irrational with justification, (i) 1.020020002.. (4) (a) *~1 1 ir. (a) 40/30 cm² (d) practical use of geometry (d) -20 (d) 141 (a) +1 2 4y-x2 4 cm² (d) none of these

193. Mathematics IX: Term -| 10. Evaluate: (97)? by using an identity. 11. Find the value ofk, ifx +3 is a factor of 3x + kx +6. lidian geometry 1S Valia only for curved surfaces. State whether this statement is true or false. Justify your answer. T wo triangles ABG and DEr, AB = DE and AC = EF. Name two angles from the two triangles that must be equal so that the two triangles are congruent. Give reasons for your answer. 1fone angle of a triangle is greater than the sum of the other two. show that the triangle is an obtuse angled triangle. or on which axis each of the following points lie? A(0, -5), B(-3, -3) 14. In which quadrant 16. Simplify: Ouestion numbers l5 to 24 carry3 marks each. 15. Represent: v3.5 on the number line Show that 3 (25)2 x (243) 5 5 (16)+ x(8) 3 12 17. Factorise: 8p+p². 5 Factorise: 3-12(2 -b) X 3 Fig. 1 9 6 P OR 25 + 19. In the Fig. 1, ifOX =XY, PX= OR 20. In Fig. 2, find x if AB|| CD||EF. 18. Determine the value ofa for which the polynomial 2r* +3*+2ax*+3x +6 is divisible by I-2%. 125 1 OR OR =1 1 Section -C A< XZ and 0X = PX, using Euclid's axiom, show that XY = XZ C 60 Fig. 2 B 140° In Fig. 3, lines XY and MN intersect at 0. If ZPOY = 90° and a:b= 2:3,find c. D Fig. 3 OVK Global Publications Pvt Ltd.

21. PrOve that the measure of each angle of an cquilateral riange 22. In Fig. 4, ifAB||CD, 21:22 = 5:4, then find 6 6 7+3 29. 23. The angles of a uriangle are in the ratio 2:3:4. Find the angles of the triangie Show that: Flg. 4 2 44. ind he arca of an isosccles trianle each of whose eual sides are 13 cm and whose base is 24 cm. Question numbers 25 to34 carry 4 marks each. 25. Ifx =- ind the value of x -2*-7x -4. 2-/3 26. Ir +2/3 = 4-V3 b, find a and b. B OR Factorise: -7-8od, 3-J8 8 -7 7-/6 v -/5 /5-2 Section –D 27. Using factor theorem, factorise the polynomial x* +*-7x-x+6. OR Model Question Papers =5 If-1 is a factor of at +-2 +6, find the values of a and b. O VK Global Publications Pyt. Ltd. 28. Find the product of (2x -y +3z) (4x? +y² +9z+2xy +3yz – 6xz).hho Disl 30. Plot the following points and write the name of the figure thus obtained: P(-1, 0), Q (2, 0), R (2, 3), S (-l, 5). Also find the arca of the figure obtained. 31. In Fig. 5,m and n are two plane mirrors perpendicular to cach other. Showthat incident ray CA is parallel to relected ray BD. 32. Prove that the angle between the internal bisector of one base angle and thc external bisector of other is equal to one half of the vertical angle. m D, 194 P 33. Prove that the angles opposite to equal sides of a triangle are cqual.. a '3Dst Flg. 5 34. In a triangle ABC, it is givcn thatAB = AC and the bisectors of ZB and ZCintersect at O. IfM is a point on BOproduced, prove that ZMOC = ABC.

Time: 3 hours Coneral Instructions: As gwen tn Model Question Paper (Unsolved) 1. 1 equals 5 +3 (a) V5-3 Ouestion numbers 1 to 8 carry l mark each. Model Question Paper (Unsolved) -3 Summative Assessment - I (a) only 3. Zeroes of the polynomial 7x-1 are 2. If b(x) =x+3, then p(*)+ p(-*) is equal to (a) 3 (6) 2x (a) a +b =0 5. If2%a +b²) = (a +b), then (a) 6V3 cm Mathematics 9. Simplify: (6) V5 +V 4. Euclid stated that all right angles are equal to each other in the form of (b) a definition (a) an axiom 10. Factorise: 216x 8. In APOR, if ZR = 22, then (a) QR>PR -2 + O VK GIlobal Publications Pvt. Ltd. (b) ab = 0 1 6. The side of an isosceles right triangle of hypoteneuse 6/2 cm is 125 Section - A (6) 6 cm Question numbers 9 to 14 carry 2 marks each. 3. (c) V5 -3 (b) 372 cm? (6) PQ =PR (c) 0 2 (c) only (c) a postulate (c)a= b -1 7. The area of a parallelogram ABCD whose adjacent sides measure 34 cm and 20 cm and the diagonal AC measures 42 cm is (a) 336 cm? (c) 8 cm Section- B (c) 420 cm? (c) PQ<PR Maximum Marks: 90 (d) V5-3 (d) 6 16 (d) a proof (d) 2a = b (d) 12 cm (d) 672 cm? (d) QR<PR

196 Mathematics IX: Term -I 11. Determine the remainder when the polynonial p(*)=x - 3x+2* +1 is divided by x -1. 12. The statements that are proved are called axioms. State whether the statement is true or false. Justify your answer. 13. Find the coordinates of a point which lies: (0) below *-axis and on y-axis at a distance of 6 units. (2) to the right of origin and on x-axis at a distance 6 units. 14. In Fig. 1, if AB||CD, ZAPO = 50° and ZPRD = 127°, find x and y. In Fig. 2, show that AB > AC. 3 16. Simplify: /81 -8216+15/32+225. Question numbers 15 to 24 carry 3 marks each. 15. Locate /13 on the number line. 5 find the value ofk. OR x+2 A X, P OR Fig. 1 Fig. 3 17. Ifx =is a root of the polynomial f(x) = 6x-1lx+kx -20, find the value of k. OR 18. Using a suitable identify evaluate (104). find the value ofx. R 1 If the polynomials ky +4y +3y -4 and y-4y +*leavethe same remainder when divided by (y-), Section - C 2 B 127° 20. In Fig. 4, if AB|| CD, find the value of x. 19. In Fig. 3, we have BX =AB, BY = BC and AB = BC. Using Euclid's axiom, show that BX = BY. B 105° Fig. 4 D 25° 21. In Fig. 5, APLQR,PR> PQ and PS = PQ, Show that AR>A0. 120° E P Fig. 2 110° Fig. 5 R VK GIobal Publications Pvt. Ltd.

24. randFare respectively the mid-points of equal sides AB and AC of AABC. Show that BF= CE. 99. AD and|BC are equal perpendicular to a line segment AB. Show that CD bisects AB in Fig. 6. 93. In Fig. 7, find the value ofx. OR -6 5+/6 Ouestion numbers 25 to 34 carry 4 marks each. 25. IF5-y Ifa =3-2/2, find a" +g 27. Factorise: =a-b/6, find the values ofa and b. OR 64 125 A Fig. 6 96 -a-8- a+ 25 Find the perimeter and area of a triangle whose sides are of lengths 52 cm, 56 cm and 60 cm respectively. 26. If,2 = 1.414 and /5 = 2.236, find the value of. OR Factorise: z+3z +3z-7. BC = DE. C 48 5 29. Factorise: x+13x +32x +20. Section - D1 -a. 28. Ifa+p=2, prove that a° +6ap + p° -8 =0. Model Question Papers 31. Prove that the angles opposite to equal sides of a triangle 30. Plot the following points and check whether they are collinear or not: (1, 1) (2, -3) (-1, -2) 32. In Fig. 8, Z0Q> R, PS is the angle bisector of the ZQPR. PMLQR. Prove that MPS =15°. 35° 33. A riangle ABC is right-angled at A. AL is drawn perpendicular to BC. Prove that /BAL = ACB. 2 V10 -5 up tothree places of decimal. 2\/2 are equal. 34. In Fig. 9,AC = AE. AB = AD and BAD = EAC. Show that 45° E B Fig. 7 iP. G30 80 M S Fig. 8 197 Fig. 9 s0°/ R

Time: 3 hours General Instructions: As given in Model Question Paper (Unsolved). 1. Every rational number is Question numbers 1 to 8 carry l mark each. (a) a whole number (a) 0 (a) 2 Model Question Paper (Unsolved) -4 Summative Assessment - l 2. When the polynomial y +3y² +3y +1 is divided by y +l, the remainder is (a) 0 3. The degree of the polynomial (* +9)(5-*2) is (a) 84 cm2 4. The number of dimension a point has is (a) 10 cm (a) 0 2 Mathematics (6) a natural number (6) 4 8. Angle x in Fig. 1. is (a) 30° (c) 40° (b) 1 5. The area of a triangle whose sides are 13 cm, 14 cm and 15 cm is (6) 1 (i) a rational number 10. Expand (4a -b+2c)*. Section -A (b) 168 cm² (b) 20 cm (6) 1 (d) -1 (c) a real number 7. If+ =1, (a 0, b 0), then the value of a +b is b (b) 50° (d) 60° (c)–4 6. If the area of an equilateral triangle is 25/3 cm², then the perimeter of the triangle is Question numbers 9 to 14 carry 2 marks each. (c) 4 (c) 2 (c) 91 cm? (c) 30 cm B Section - B 9. Give an example of two irrational numbers whose product is (ü) an irrational number 45° 105° Maximnum Marks: 90 Fig. 1 (d) an integer eh (d) 2 (d) 0 (d) 3 (d) 105 cm? (d) 40 cm D

11. Evaluate 105 X 106 using an identity. 19. Write the coordinate of the point where x-axis and y-axis intersect. Also find the coordinate of a point whose ordinate is -5 and which lies on y-axis. 13. "For every line l and for every point pnot lying on a given line l, there exists a unique line m passing through pand parallel to l" is known as Play fair's axiom. Is the above statement true or false? Justity your answer. 14. In triangles ABC and PQR, A = LP, B = LQ and AB =QR will the two triangles be congruent? Give reasons for your answer. 17. In Fig. 2, AB and CD bisect each other at 0. Prove that AC= BD. Ouestion numbers 15 to 24 carry 3 marks each. 15. Express 0.0032 in the form of, where p and g are integers and q 0. 16. Represent N93 on the number line. OR OR 2 If 3 =1732 and y2 = 1.414, then find Section-C Find the remainder when b(x) = 4x-12x +14x-3 is divided by g«) =x 18. Factorise: 8x +27y +36xy +541y². OR Simplify: (2x +p-)*- (2*- p+q) Model Question Papers values of a andb. 19. In Fig. 3, we have ZABC = ZACB, Z3 = 24. Using an Euclid axiom, show that 1=Z2. 20. In Fig. 4, ifx +y = w +z, then prove that AOB is a line. In Fig. 5, AD = AE and ZBAD= ZCAE. Prove that AABC is isosceles. B VK Global Publications Pvt. Ltd. A Fig. 5 21. S is any point in the interior of APQR. Show that SQ +SR < PQ +PR. i tott tnsti 22. In Fig. 6, ZAOC and ZBOC form a linear pair. If a-b= 20°, find the Fig. 2 A Fig. 3 Fig. 6 199 3 2 x Fig. 4 D B

200 23. In Fig. 7, AM and DN are the medians. Then tind the value of DF. Mathemotics IX: Term -I 24. A rhombus shaped ficld has grass for 18 buffaloes to 25. ELe 8raze on. If each side of the rhombus is 30 m and its longer diagonal is 48 m. how much area of the field will cach buffalo graze on, ifall the buffaloes on equal arca. Question numbers 25 to 34 carry 4 marks each. find the value of 2%-7x-2x +1. 29. 30. Ifx = 26. Simplify the following expression: (V3 +1)(1-/12)+ 2+/3 OR 27. Factorise: r'+3r+3r-7 Rationalise the denominator of the following: 4V3 +52 /3 +/12 V48 +/18 28. Factorise: (*²-y)² +(y? -z2)+(z?-*2)2. Section - D OR Factorise: x -7x-8. 2 (i)(-3, -5) () (3, -5) (iiü) (-4, 5) Also, verify by locating them on the cartesian plane. Write the quadrant in which each of the following points lie: 32. In Fig. 8, bisectors of ZB and D of quadrilateral ABCD meet CD and 4 cm AB produced at P and Q respectively. Prove that LP+ LQ-(LABC+ LADC). A Without actualdivision, prove that 2x –5x +2*-x+2 is divisible by x-3x +2. B 23. IfD is the mid-point of the hypotenuse AC of a right-angle triangle ABC, then prove that P BD =AC. 6 cm M 4S cm (iv) (3, 4) 31. Prove that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. D C Fig. 7 Flg. 8 E B 34. If the altitudes from the vertices of a triangle to the opposite sides are equal, then prove that the triangle is isosceles. VK Global Publications Pvt. Lta.

Time: 3 hours Ceneral nstructions: As given in Model Question Paper (Unsolved) 1. (a) 3 Question numbers I to 8 carry l mark each. 1. Value of (8 1) x (81)0.09 is equal to (a) -5 (a) 1 2. The degree of the polynomial (*+5)(4 -*) is (a) 0 Model Question Paper (Unsolved) -5 Summative Assessment - (a) remains the same (a) 100 m g Jf(: +1) is a factor of the polynomial x- +k, then the value ofk is 4. The number of dimensions, a solid has is a+b is (b) 9 (a) -7 Mathematics 5. If the sides of a triangle are trebled, then its area (c) 14 (b) 2 (a) 80° (6) 0 (c) 60° (b) 1 Section -A OVK Global Publications Pvt Ltd. (6) becomes two times (b) 160 m (b) 7 (d) – 8 (6) 70° (a) 50° (c) 27 6. The sides of a triangle are in the ratio 16: 18:25 and its perimeter is 590 m. The smallest side of the triangle is Question numbers 9 to 14 carry 2 marks each. (C) 3.: 9. Find two rational numbers between -l and (c) 2 (c) 2 2 0 7. If (* +2)'and (x -2) are factors of ax +2*-3x+ bx -4, then the value of (c) becomes three times (c) 180 m Section -B Maximum Marks: 90 8. In Fig. 1, BO, CO are the bisectors of external angles CBE and ZBCD respectively of A ABC. Then ZBOC is equal to (d) 81.25 10. Find the value of5 +7+(-12) without calculating the cubes. (d) (d) -2 (d) 3 (d) becomes nine times (d) 250 m i B i A Fig. 1

202 Mathematics IX: Term -1 11. Expand: (3a-5b-c)'. 12. Which of the following points. do,not 1he on w 9zest Where d thhef e A(-2, 3), B(0, -4), C(5, 0), LD(-3, -5) 13. In Fig. 2, find the value of for which the lines I and m are In Fig. 3, if AB ||CD, Z1 : 24 = 3:2, then fínd 6. 14. The edges of a surface are curves. State whether the statement ís true or false, Justity yor T5me OR and b OR Question numnbers 15 to 24 carry 3 marks each. Locate V17 on the number line. 2-V5 16. Ifa = 2+/5 15. Express the decimal number 2.218 in the forn of,q0. 2+V5 2-F 17. Factorise: 2x +3/5x +5. Flg, 2 OR 445 find a?-52 18. Evaluate (103) by using an identity. Section -C Factorise: 16x+4y+9z-16xy-12yz + 24L. 20. In Fig. 4, AB || CD, Determine x. OR 19. It is known that x +y =10 and that x = z. Show that z +y = 10. Solve the question usíng appropriate Euclid's axiorm. 21. Prove that the bisectors of angles of a linear pair are at right angles. D 4cm AABC and ADBC are two isosceles tríangles on the sarme base BC. Show that ZABD=ACD. 22. In Fig. 5, if line l is the bisector of LA, then find 02 Fg. 5 Fia, 4 VK Globat Publications Pn L0

23. In AABC, (Fig. 6), 4AB = AC and AD is angle bisector of ZA. Prove AABD AACD. 24. A perimeter of a triangle is 420 metres and its sides are in the ratio of 6:7:8. ad the area of the triangie. Question numbers 25 to 34 carry 4 marks each. 25. Factorise: (2a +3b)* -(2a-36)'. Factorise: a'-!12 26. Show that: alb-c) 5+3/3 27. Ir 7+4/3 OR =1 =a+b3, find the values of a andb. OR Simplify by rationalising the denominator 2/6 6/2 843 2+V3 Nõ +V3 6 +2 4Section 1-DTOR 98. If the polynomials az +3z* -13 and 22 -5z +a leave the same remainder when divided by z +2, find the value of a. 29. Find the value of a° -86° -36ab -216, when a = 2b +6. s 30. If two lines intersect each other, then prove that vertically opposite angles are equal. 31. Prove that the sum of any two sides of a triangle is greater than twice the median drawn to the third side. 32. In Fig. 7, LM is a line parallel to the y-axis at a distance of3 units. () What are the coordinates of the points P, R and Q? (ä) What is the difference between the abscissa of the points L and M? (i) Name the point equidistant from the point R. A E Model Question Papers Fig. 8 B D Fig. 7 33. AD, BE and CF, the altitudes of triangle ABC are equal. Prove that triangle ABC is an equilateral triangle. 34. In Fig. 8, AB is a line segment and P is its mid-point. D and E are points on the same side ofAB such that ZBAD=ABE and EPA= 2DPB. Sh0w that AD = BE. Fig. 6 OM 203

Time: 3 hours General Instructions: As given in Model Question Paper (Unsolvea) (a) equal (c) unequal Question numbers 1 to 8 carryl mark each. 1. The things which are double of same thing are (a) -2 2. If (x-2) is a factor of 2x-6x +5x +c, then c is 3. The number (3 -1l)(3+V11) is (a) a natural number Model Question Paper (Unsolved) -6 Summative Assessment - ! (c) a rational number 10. (a) 2 (a) 4. The degree of the polynomial 2- y* -y° +2y' is 240 Mathematics (a) 26 (6) 2 (6) 7 (a) QP=5 cm, ZP= 60° (c) QR =5 cm, R= 80° Section -A 7. Ifa+b=-1, then the value of a +b -Bab is Expand (b) 525 5. Arhombus sheet whose perimeter is 40 m and one diagonal is 12 m long is painted on both sides at the rate of5 m². The cost of painting is (6) 3/3 cm² (6) 1 6. The altitude of an equilateral triangle is 3/3 cm. The area isisletr (a) 6/3 cm² (6) halves of same thing Question numbers 9 to 14 carry 2 marks each. 9. Simplify /81 -8/216 +15/32 +/225. (d) double of the same thing (c) 18 (6) a whole number (d) an irrational number (c) 0 (c)480tle Maxinum Marks: 90 (c) -1:st 8. Triangles ABC and PQR are congruent. If AB - 5 cm, ZB= 40° and ZA= 80°, then which of the following is true? (d) -18 (6) QP = 5 cm, ZR = 60° (d) QR =5 cm, ZQ= 40° Section - B (d) 3.ih (c) 12V3 cm² i e (d) 9/3 cm² ( (d) 960 (d) -26 VK Global Publications Pvt. Ltd.

11. Determine whether (3x -2) is a factor of 3: 3 figure so formed and write its one property. 13. In Fig. 1, ifx =61° and y =118°. Is ml|n? 12. Plot the points A (3, 0), B (3, 3) andC(0,3) in a Cartesian plane. Join OA, AB, BC and CO, Name the m Fig. 1 4 In Eig.2, AC = XD, C is mid-point ofAB and D is mid-point of XY. Using Euclid's axiom, show that AB = XY. Ouestion numbers 15 to 24 carry 3 marks each. b (ü)O is also the mid-point of BC. 1 „2 Lines PQ and RS intersect each other at point 0. If ZPOR: ZROO =5: 7 find all the remaining angles. 15. E and F are respectively the mid-points of equal sides AB and AC of AABC. Show that BF= CE. OR Factorise: 6x +5x -6 In Fig. 3, ine segment AB||CD and O is the mid-point of AD. Show that (i) AAOB ADOC. 17. Factorise: x*++2-2x -–, +x*-20x +12. OR 16. Express 0.001 in the form of , where p and q are integers and q # 0. OR 19. Simplify : (a +b+c)* -(a-b-c)*. Model Question Papers Section-C 20. Locate /5 on the number line. VK GIobal Putblications Pvt. Ltd. OR 18. Find the area of a triangular park whose sides are of lengths 120 m, 80 m and 50 m. Prove that /5 -3 is not a rational number. Z1. In Fig. 4, AB||CD. CD||EF and y :z = 3:7, find the measure of x, yC and z. B A Fig. 2 205 Flg. 4 Flg. 3 B

206 22. Mathematics IX : Term -I Show that the angles of an equilateral triangle are 60° eacl 23. Iltwo interior angles on the same side ofa transyersal intersecting two parallel lines are in the:ratio 2:3, then find the larger of two angles. ng D, ioP | RS, ZOPQ= |10° and 2ORS = 130°, then determine ZPQR. + P 110° Question numbers 25 to 34 carry 4 marks cach. 25. Evaluate: +... + /2 +1 N3 +2 4+3 Flg. 5 OR Ifx =2+/3, find the value ofx+. Factorise: x -64 OR Section-D 26. Simnplify the following by rationalising the denominator: /9 +8 R 130° 27. Ifthe polynomials ax +4x+3x – 4 and x-4x +aleave the same remainder when divided by (x -3). find the value ofa. 28. In Fig. 6, AC = BC,ZDCA = ZECB and ZDBC = ZEAC. Prove that (i) ADBC AEAC(ii) DC = EC and BD = AE. AC 29. Ifa +b +C=9 and ab +bc + ca = 40.finda'+2 +. Flg. 6 S 6–4/3 6+4/3 Di. Esis E © VK Global Publications Pvt. Lt.

From the Fig. 7, write 5 B (0) the coordinates of the points B and E. (m) the abscissa of the points D and H. (v) the quadrant in which points B and I lie. (ui) the perpendicular distance of the point G from the x-axis. (uin) the perpendicular distance of the point I from the y-axis. Fig.7 <QTR1 (vii) the point whose perpendicular distance from y-axis is 2 units. 31. Prove that the sum of the angles of a triangle is 180°, 2 JZ. D is a point on side BC of AABC such that AD = AC. Show that AB > AD. in ig. 8, the side QR of APOR is produced to a point S. Ifthe bisectors of PQR and meet at point T, then prove that QPR. Model Question Papers (i) the point identified by the coordinates (1, 1). (iv) the ordinates of the points A and C. PRS VK Global Publications P Ltd. Q P 207 Ri Fig. 8 34. Without actual division, prove that (2x -6x+3+3r -2) is exactly divisible by (r*-3r +2).

Time: 3 hours General Instructions: As given in Model Question Paper (Unsolved): Model Question Paper (Unsoived) -? Summative Assessmert - I (a) 1 Question numbers 1 to 8 carry l mark each. 1. Ifx +kx +6 = (* +2)(x +3) for all x, the value ofk is Mathematics (b) – 1 (c) 0.101001000100001... (a) 60 cm 2. Which of the following is a rational number? (a) V5 (b) 48 cm 5. If*+=62, then + (6) 3415 3. The lengths of the sides of a triangle are in the ratio 3 :4:5 and its perimeter is 144 cm. The height of the triangle corresponding to the longest side is (c) a right triangle Section -A (a) 512it el tl () 488 equals (a) an acute angled triangle (6) p(-b la) 4. An isOsceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Its area is (a) 9/15 (c) 5 (b) Tt (d) 0.853853853... (a) A line segment has definite length 6. When p(¢) is divided by ax -b, then the remainder is (a) pla + b) (c) 28.8 cm (c) 9V14 7. The angles of a triangle are in the ratio 5:3:7. The triangle is Question numbers 9 to 14 carry 2 marks each. 9. Evaluate: (343)-2 (c) pla/b)iixs (c) 504 ios 2sh (d) 498 8. Which of the following statements is incorrect?. (d) an isosceles triangle (6) Three lines are concurrent if and only if they have a common point Maximum Marks: 90 (d) 3 (b) obtuse angled triangle (c) Two lines drawn in a plane always intersect at a point. Section - B (d) 36 cm (d) 9V13 (d) pbla) (d) One and only one line can be drawn passing through a given point and parallel to a given line. OVK Global Publications Pvt LIO.

10. Factorise: 7/2x-10x -4 1 Ifa+b+c=7and ab +bc + ca= 20, find the value of 2 +)'+c. 19 In Fig. 1, if AB||CD, then find the value of x. 1 (i) Coordinates of point A (2) Abscissa of point D fF 13. In Fig. 2, ZPQR=PRQ, then prove that ZPQS = ZPRT. Q/2r- 10° OR 14. See Fig. 4, and write the following: L P Fig. 1 VK Global Publications Pvt. Ltd. In Fig. 3, sides QP and RQ of APQR are produccd to point S and T respectively. If ZSPR=135° and ZPQT =110°,find ZPRQ, OR Locate W4.7 on the number line. 5x-20° -2 -3 -1t -5 y +4 5 +3 -4+ F2 B Fig. 4 (ii0) The point identified by the coordinates (5, 4) (iv) Coordinates of point C. Question numbers 15 to 24 carry 3 markS each. 15. Represent /5 on the number line. 1. 2 34 345 6 7, X B:6 Section -C Model Question Papers S T 110° Fig. 2 Fig. 3 R 209 4S T I35" R

210 16. Express 5.347in the form 2 where and a are integers arnd g #U Mothematics IX :Term -| 17. Factorise: 2J243 18. +863 -27c +18/2abc. OR 23. Factorise: (ax + y) +(ay - bx), rIg 2, D 1s a point on side BC of AABC Such that AD = AC. Show te AB> AD. 1S. In ig. 6, ZX =72°,ZXZY 46°.IfyO andZ0 are bisectors of XYZ and zz respectively of AXYZ, find Z0YZ and ZYOZ. OR 72 Fig. 6 In Fig. 7, AD = CE are the angle bisectors of ZA and ZC respectively. If ZABC =90°, then findZAOC. 20. Find the value of 64x +1252, if4x +5z= 19 and xz = 5. A 21. In AABC, BE and CF are altitudes on the sides AC and AB respectively such that BE = CF. Using RHS congruency rule, prove that AB = AC. In Fig. 8, OD is the bisector of ZAOC. OE is the bisector of ZBOC and OD LOE. Show that the points A, and B are collinear. 22. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the base l5 cm, find the height of parallelogram. c Fig. 8 V5 +/3 V3 +/2 V5 +V2 26. Ifa=7-443, find the value of va + 24. In Fig. 9, if AC is the bisector of ZA and 2C and A= 3, show that ZA= LC. Question numbers 25 to 34 carry 4 marks each. 2 25. Simplify: B Va Fig. 5 Section - D D Fig. 7 C Fig. 9 VKGlobal Publications Pt. Ltd.

27. Find the values of a and b ir7+345 :7-3/5 Ci 3+V5 3-5 OR Which of the following points lie on the negative side ofx-axis? Which of them lie on the posiive side of y-axis? (-2, -2), (-4,0), (-3,2), (0, -4), (5,-7), (1,3), (-6,-5)(3, -2) Which of the above points do not lie in any of the quadrants? 29. Simplify) 98. The polynomial () =**-2%° +3x - ax +3a-7 when divided by (x +1) leaves the remainder 19. Find the value of a. Also find the remainder, when b(x) is divided by x +2. =04: Find the values of a and b so that (* +1) and (* -1) are factors ofx +ax-3x+2x +h. 3 OR 20 Prove "If twolines intersect each other, then the vertically opposite angles are cqual". that AB = AC. (ü) Factorise: a + b–2(ab- ac +bc). 31. In Fig. 10, the sides AB and AC of AABC are produced to points E and D respectively. If bisectors BO and CO of ZCBE and ZBCD respectively meet at point O, then prove that BOC=90°BAG. © VK Glebal Publications Pvt. Ltd. B Model Question Papers A 32. () Muliply 9x* +25y* +15xy +12x -20y +16 by 3x -5y -4 using suitable identity. Fig. 10. D C 211 33. In Fig, 1I,D and E are points on the base BC of a AABCsuch that 4D = AE and ZBAD = ZCAE. Prove Flg. 11 2 34. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD, show that ZA> LC and ZB> ZD.

Time:3 hours General Instructions: As given in Model Ouestion Paper (Unsolved)-1: 1. The number (2 -/6)(2 +V6) is is Question numbers 1 to 8 carry l mark each. (a) 9 (a) a natural number (6) a whole numberso t(c) a rational number (a) first axiom 2. The numerical coefficient of y in (3x -) isg i: 4. x +is MOdel Question Paper (Unsolved) -8ha Summative Assessnent - (a) a polynomial of degree 1 (c) a polynomial of degree 0 (a) 1 (a) 54/3 cm² 3. It is known that ifx +y =l0,then x +y +z=10 +z. TheEuclid's axiom that illustrates this statemment is (b) second axiom Mathematics of the triangle is (a)27 cm? (c) 54/7 cm² (6)– 27 () a+c +e=1 80° (a) only (Ö) bi (6)- 1 (c) only (üi) 5. Which of the following numbers is not a zero of the polynomial 2x * +9x +llx + 4x -6? 6. The height of an equilateral triangle measures 9 cm. Its area is Section -A (ii) iheant (6) 144/3 cm? (b) 27/7 cm² (d) 54 cm? (c) -1 b +f = c+e (b) only (ü) (c) third axiom 7. The perimeter of an isosceles triangle is 42 cm and its base is times each of the equal sides. The area 8. In Fig. 1, which of the following statements must be true? (c) -3 (d) both (i) and (ü) (6) a polynomial of degree 2 (d) not a polynomial (c) 27/3 cm² Maximum Marks: 90 (d) an irrational number (i2) a +b=d +c (d) - 9 Fig. 1 (d) fourth axiomn (d) 3 (d) 108 cm?

Question numbers 9 to 14 carry 2 markS each. 10. o Find two irrational numbers betweenand 11. Expand Find the value of a if (x -a) is a factor of x-a'x +x +2. 2 8 si sSection B 16. Ifa = 12. Are there any points in the cartesian plane which do not belong lo any quadrants? If so, name such points. 2+/5 2-/5 15. Locate /4.5 on the number line. Simplify: 13, In Fig. 2, the sides BC,CA and AB ofa ABC have been produced to D. E andr respectively. If ZACD = 105° and EAF = 45°, find all the angles of AABC. Question numbers 15 to 24 carry 3 marks each. and b If the supplement of an angle is four times its complement, find the ngle. 14. In ADEF, D =70° and E =30°, which side of this triangle is the longest? 2V6 2-45 2+/5 17. Factorise: 2x +432*y OR 642 B Factorise: 8(x + y)-27(x - y) © VK Global Publications Pvt. Ltd. 2 OR 3 then find the value ofa' -b. 8/3 OR 18. Evaluate 108 using a suitable identity. 4 135° Section -C Fig. 3 OR Model GQuestion Papers of' the In Fig. 4, if l, || l, and 1||l4, find y in terins of a. E 45/ 19. If a point lies between two points P and R such that PQ =QR, then prove that PQ =-PR. Fig. 2 ) 2 20. In Fig. 3, if the bisectors of base angles ofa triangle enclose an angle of 135, prove that the riangle is ia right triangle. 105° Fig. 4 213 D

214 21. If the bisector of the exterior vertical angle of a triangle is parallel to the base, show that the trianglei Z3. Mathematics X : Term -1 22. In Fig. 5, If AB||CD||EF, PQI|RS, . Z4. isosceles. 26. A 25. Simplity: (25)2 x (243)5 70\/Q O Is alny point in the interior ofAABG. Prove that AB +BC +CA>0A +0B +0C. (L6)4 x (8)3 Find the value of. Ihe lengtlh of the sides ofa triangle are in the ratio of3 :4:5 and itsperimeter is 144 Cn. Find the area of the triangle. Also, find the height corresponding to its longest side. Question nunbers 25 to 34 carry 4 marks each. OR Ifx =3+8,find the value ofx+ 29. Factorise: )" + pg 30° 4 Fig. 5 /3-/2-l 4 OR ZRQD =30° and ZCQP R B 27. If() =**-58 +7, evaluate f2)– f-) +f Section - D 28. IfVm +u-p=0, then find the value of (m +n - p)² +1+2þ+9 Correct to the three places of decimal if 2 = 1.414 and /6 =2.45 = 70°, then find QRS. Factorise: (2a-36) +(36–4c) +(4c- 2a) 30. In Fig. 6, PTLQR and PS is the bisector of ZP. I! 20=60° and ZR=30°, findZTPS. 60° Fig. 6 30 R ©VKGlobal Publications Pvt. Ld

B 31. In Fig. 7, Side BC of a AABC is produced to a noint n The bisector of ZA meets BC at L rove LABC +ACD =2/ALC Fig. 7 32. In Fig. 8, PORS is a quadrilateral where PQ = RO, ZPQT= ZRQU, LTOS = ZUQS. Prove that QT =QU. B Model Question Papers 33. In an isosceles triangle ABC (Fig. 9), AB AC. bisectors of ZB and 2C intersect each other at 0. Show that (i) OB = OC (ü) AO bisects ZA. A Fig. 9 R U 215 Fig. 8 34. On plotting the points A(1,0), B(5, 0), C(5, 4) and D(1, 4) and joining AB, BC, CD and DA, which tigure is obtained? Find its area.

Time: 3 hours General lhustructions: As given in Model Queslion Paper (Unsolved) a 2. Question uumbers 1 to 8 carry l mark each. 1. A rarional nunber between /2 and V3 is 5. 6. (a) 8. (a) -2 3. V7 is a polyuomial of degree Model Question Paper (Unsolved) - Summative Assessnent - 9. (a) ) The value of polynomial 3x-5x +2 al x =is 4. Which of the following needs a proof? (b) Definition u) Axiom (6) I.52 The area of a rhombus (u) 384 m Mathematics (6) (u) x ++x+x +1 IL is given thatAABG Lrue? (6) I Section -A 7. Which of the lollowing polynomials has (x +I) asa factor? (C) DE=t.6 cm, Z=70° (u) DE = 4.6 cm, Z) = 70° (c) 1.92 (0) x +x*+x +1 (c) (c) 7 The area of a triaugle whose sides are 35 cm, 45 cm and 50 cnn is (u) 75,6 cm² (6) 75/13 cm² (c) 25/13 cm² whose perimeter is 80 m and one of whose cliagonal is 24 m is (b) 192 m² (c) 960 n' (d) 520 m² Questivn numbers 9 to 14 carry 2 marks cach. Fil two irrational ounbers whosc sum is (1) a rational number (c) Theorem Maximum Marks: 90 Section - B (ed) (c) x+2x-2x +1 (d) x +3+3x +x +l ADEF and AB =4.6 cm, ZB = 60°and ZA =50°.Then wlhich ofthe followiug is (d) 1 (iü) an irrativnal nunber 2 (d) Postulate (b) DE =4.6 cIn, ZF =70° (d) DF =4.6 Cm, Z = 60° (ed) 150/26 cm² VK Global Publications Pvt Lio

10. Factorise: 492 11. Give possible expressions for the length and breadth of the rectangle whose area is a2 14. 4 -3a +2. answer. 12. If one of C the angles formed by two intersecting lines is a right angle,i4y what can you say about the other three angles? Give reason for your Find x andy il 7,||2, in Fig. 1. 13. In Fig. 2, find ZDAC. 120° A + OR 3/3 -2/2 343 +2/2 Ouestion numbers 15 to 24 carry 3 marks each. 3 15. Simplify: 16. Express 23.43 in the form D OR Fig. 2 Ifx =3+2/2, find the value of Vx - The base BC of an equilateral riangle ABC with side BC = 8 units lie along x-axis such that the mid-point of the base is at origin. Find coordinatesofB and C. Also find coordinates of third vertex A, ifA lies along positive direction ofy-axis. © VK Global Publicatons Pvt. Ltd. 20° OR Model Guestion Papers Section -C 17. If3x -7y = 10 and xy =-1, find the value of 9x + 49y* Find the value of 4x+y²+252 +4xy -10yz -20zx, using the identity if X =4.y =3,z=2. 18. Find the value of1009' using a suitable identity. 19. In ABC,ADL BC and AE bisects ZA. If ZB =45° aud ZC = 25°, tlhen fiud ZDAE (+ 2y): 20. In Fig. 3,ZABC =80°,ZEFG = 45°:and ZEGF =35°. P'rove tat 1B|| DE. 21. Arav and Kaay bave the sane height. If their heights increase by5 cm cach, how will their new heights be compared: 108° Fig.1 217 35° Fig. 3 45° 80

218 Mathematics IX : Tem -I *etnat the length of the peTDendicnlars drnwn from vertices ofequal angiesN of an isOSceles riangle to the opposite sides are cqual. In Fig. 4, 4 Aand OE = OF, Prove that OC = 0B. 23. In Fig. 5,ACLCE and ZA: ZB:2C=5:3:2, Find ZEGD. 1 26. Ifyz =l, show that 27. Simplify: ** O adjacent sides ofa parallelogramare 5 cm and 3.5 cm, One ofits diagonals is 6.5 cm. l'ind the are of the parallelogam. Question numnbers 25 to 34 carry 4 marks each. 25. If: + =119,find Simplify: -$ ge-OR 2187 7 956 4 Factorise: x -64. A + 1 +*+y l++z A OR Fig. 5 (1331) 3 OR 2 1 Section - D 29. Using factor theorenm, factorise the polynomialx°+x*-4x-4. S 28. Ifx+ax* + bx +6 has (x -2) as factor and leaves remainder 3 when divided by (x-3), fumd the valucs of a andb. Fig. 6 1 I+2+! 30. Prove that if two lines intersect cach other, then the vertically opposite angles are equal. 31. In Fig. 6, APl and PR> PQ. Show that AR> AQ. =1. C 3 R Flg. 4 VKGlobal Publications Pvt. LU

32. In Fig. 7, , the side QRof APQR is produced to point S. If the bisector of ZPQR and ZPRS meet at point T. then prove that ZQTR=0 R VK Global Publications Pvt. Ltd. Fig.7 33, Plot the following points and check whether they are collinear or not: (6, -2), (1, 3), (–2, -4), (-l, 5) A- NoUDs D, 94. In Fig. 8, ABCD is a square. M is the nid-point of AB and PQ LCM. Prove that CP =CQ Model Question Papers M Fig. 8 3 219 -(0)

Time: 3 hours General Instructions: As given in Model Question Paper (Unsolved) 1. Question numbers 1 to 8 carry l mark each. 243 32 (a) 32 243 8. (a) 15 4 Model Question Paper (Unsolved) -10 Summative Assessmnent - (a) 125 is equal to 2. If p(r) =**+2/2x-1, then p(2/2) is equal to (b) -1 3. One of the factor of (25x -l) +(1 +5x) is (a)5 +x (6) 5 -x 4. The coefficient of y in the expansion of (5-y) is (6) 5. Boundaries of surfaces are (a) points Mathematics (c) l14 cm² 6. In AXYZ, if XY < XZ, then (a) X Y (6)– 1 (a) bya'b2 (c) by2a-62 (b) lines 7. In Fig. 1, the area of quadrilateral ABCDis (a) 102 cm? (6) LZ< Y Section - A (b) 57 cm² (d) 95 cm' (b) 2%/a-b2 (d) bya?262 (c) 16 Question numbers 9 to 14 carry 2 marks each. 81 (c) 0 The area of an isosceles triangle, the mcasure of one ofwhose cqual sides is a units and third side is 2b units is (c) 5x –1 (c)– 75 (c) curves (c) ZY < L Section -B Maximnum Marks: 90 (4) 81 16 (d) 7 (d) 10x (d) 15 (d) surfaces (d) ZY X 17 cm 15 cm Fig. 1 9 cm 12 cm 9 There is a Dumber x such that x is irraLional bul x is rational. Is the statement true? Iustify your answer by an example. ©VK Global Publications Pyt. Ltd.

10. Check whether b(*)=x-x+l is a mnultiple of g(x) =2-x or not.os fue 1tcti2 st 11. For what value oft, 2x -3 is a factor of2x-9* + px +12. 12. In which quadrant or on which axis each of the following points lie? (-5,7), (6, 0), (-1, -1), (8, -5) 13. In the given Fig. 2, 'a' is greater than 5' by one-sixth of a straignt angees a as/ Find the value of a and b. 14. Atransversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel? Justify your answer. 15. Express 0.3178in the form Question numbers 15 to 24 carry 3 marks each. ls it possible to construct a trianigle with lengths of its sides as 10 cm, 9 cm and 4 cm? Give reason for your answer. Find the values of a and b if 18. If? of 16. Ifa=5+2/6 and b =, then what will be the value of a' +62? Factorise: 27x-y-1-9xy OR 4 1 17. Factorise: 25x+16y +4z"-40x) +16yz -20:xz OR +=62, find the value of x 3 A 3-/5 D = av5 3+2/511 Model Question Papers 4 Section -C Fig. 3 19. Solve the equationx +8 = 1l and state which axiom do you use here. ii 20. In Fig. 3, we have ZABC=ZACB and Z3 = 24. Show that 1= /). 2 b + 3 Fig. 2 21. AP and BQ are the bisectors of two alternate interior angles formed by the intersection of a transversal n with lines l and n (see Fig. 4). If AP||BQ, show that l||m. 221 A Fig. 4

222 Mathematics |X : Term -| 22. Show that the sum of the three altitudes ofa t Ln quadrilateral ABCD, AB is the longest and CD is the shortest side. Prove that ZC>ZA and ZD> B. OR 23. In Fig. 5, if Z =Zy and AB = CB,prove that AE =CD. 24. Find the cost of levelling a ground in the form ofa triangle having te sides 51 m, 37m and 20 m at the rate of {3 per m". Section - D Question numbers 25 to 34 carry 4 marks each. 25. Prove that (a +b+c) -a-b-c=3(a +b)(6 +c)(c +a) 28. Simplify: Simplify: (* + y)-(* -) -6y(* +y)(* - y) <0. Without actual division, prove that 2x4-5x +2x 2-x +2 is divisible by x -3x +2. 27. Simplify: (3x +4y) -(3x -4y) (a) 1.01 0010001 triangle. triangle is less than the sum of three sides of the t OR 4/2 3V5 5/3 V15 -3/2 V10-V3 V6 +V5 (b) + 29. Classify the following numbers as rational or irrational with justification: V28 V343 (c) 1.2555.. OR 31. Prove that if arms of an angle are respectively parallel to the arms of another angle, then the angles are either equal or supplementary. In AABC(Fig. 6), the sides AB and ACofAABC are produced to points E and D respectively. If bisectors BO and CO of ZCBE and ZBCD respectively meet at point 0, then prove that ZBOC = 90°-LA. 2 D 32. Side BC ofa AABC is produced to a point D. The bisector ofZA meets BC at L. Prove that ZABC +LACD =2/ALC. E 30. Three vertices of a rectangle are (-2, -5), (6, -5) and (6, -1). Plot these points and find the Coordinates of the fourth vertex. Also find its area. BA Fig. 5 (d) 1.350355035550... A A Fig. 6 33. Prove that the angles opposite to equal sides ofan isosceles triangle are equal. Using the above, find 2B in AABC with AC = BC in which ZC =50°. 34. Ina right triangle, prove that the line segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.